Spatial asymptotics and strong comparison principle for some fractional stochastic heat equations

Mohammud Foondun, Eulalia Nualart

Consider the following stochastic heat equation, \begin{align*} \frac{\partial u_t(x)}{\partial t}=-ν(-Δ)^{α/2} u_t(x)+σ(u_t(x))\dot{F}(t,\,x), \quad t>0, \; x \in R^d. \end{align*…